A company run by one of Italy's richest men has bought a 1,751-cabin cruise ship that was originally being built for Muammar Gaddafi's regime.

Gaddafi's fourth son, Hannibal, suggested the Libyan state-owned General National Maritime Transport Company order the 140,000-tonne vessel in 2010 to kickstart a luxury cruising industry.

The €550m (£460m) liner, which boasts four swimming pools, 26 lifts, a bowling alley and 21 bars across 18 decks, was due to be named the Phoenicia after the ancient civilisation that first settled in what is now Libya.

At the launch of the construction of the ship, which at 333 metres is longer than the Eiffel Tower is tall, Captain Ali Belhag, chairman of the transport company, said: "We believe this is a significant milestone for our introduction into the cruise industry market." He thanked Hannibal Gaddafi for his part in the project.

The ship, due for delivery to Tripoli in December 2012, would have been the world's first cruise ship owned by an Arab company. But the transport firm failed to keep up with payments to STX, the French shipyard building the liner, after the overthrow of Gaddafi.

STX, which is in the final stages of completing the ship in St Nazaire, western France, cancelled the order in June and has announced the sale of the ship to Italy's Mediterranean Shipping Company.

MSC, founded by its billionaire chief executive, Gianluigi Aponte, in 1970, is one of the world's largest shipping companies with more than 460 vessels.

Pierfrancesco Vago, the head of MSC's cruise liner subsidiary MSC Cruises, said the new ship, which will be renamed the MSC Preziosa, "represents the highlight of European cruising".

In 2008 he and his wife Aisha were arrested at a luxury Swiss hotel following allegations that they were mistreating their staff. The incident spiralled into a diplomatic row when Libya vowed to take "an eye for an eye and a tooth for a tooth" and in retaliation took two Swiss nationals hostage, suspended visas for Swiss nationals and forced Libyan branches of Swiss companies, including Nestlé, to close.

The charges of bodily harm, threatening behaviour and coercion were later dropped.

In 2001 Hannibal pleaded diplomatic immunity after attacking three police officers guarding his luxury Rome hotel room with bottles and a fire extinguisher.

In 2009 police were called to Claridge's hotel in London after reports of a woman screaming. When they arrived, the £4,000-a-night suite was locked and three bodyguards were arrested for obstructing entry. A woman understood to be his wife, a Libyan model, was found bleeding heavily and taken to hospital where she was treated for facial injuries.

MSC Cruises said the ship would also include 69 yacht club suites with access to a private bar, solarium, hydro-massage pools and glass-walled observation lounge. A butler service would offer assistance at check-in, transport luggage, unpack, serve traditional English afternoon tea as well as arranging cigars and beverages, booking tables at restaurants, treatments in the MSC Aurea spa, ad hoc excursions and even arrange private parties.